Question

Tính

1, \(\sqrt{3+2\sqrt{2}}\) 7, \(\sqrt{10-2\sqrt{21}}\)

2, \(\sqrt{4-2\sqrt{3}}\) 8, \(\sqrt{11+2\sqrt{18}}\)

3, \(\sqrt{5+2\sqrt{6}}\) 9, \(\sqrt{14-2\sqrt{33}}\)

4, \(\sqrt{7-2\sqrt{10}}\)

5, \(\sqrt{15-6\sqrt{6}}\)

6, \(\sqrt{8+2\sqrt{15}}\)

các bạn ơi ! giúp mik với đi

Answer 1

Bạn chỉ cần tách chúng thành hằng đẳng thức sau đó áp dụng HĐT: \(\sqrt{A^2}=\left|A\right|\)

1, \(\sqrt{3+2\sqrt{2}}=\sqrt{2+2\sqrt{2}+1}=\sqrt{\left(\sqrt{2}+1\right)^2}=\left|\sqrt{2}+1\right|=\sqrt{2}+1\)

2, \(\sqrt{4-2\sqrt{3}}=\sqrt{3-2\sqrt{3}+1}=\sqrt{\left(\sqrt{3}-1\right)^2}=\left|\sqrt{3}-1\right|=\sqrt{3}-1\)3, \(\sqrt{5+2\sqrt{6}}=\sqrt{3+2\sqrt{3}.\sqrt{2}+2}=\sqrt{\left(\sqrt{3}+\sqrt{2}\right)^2}=\left|\sqrt{3}+\sqrt{2}\right|=\sqrt{3}+\sqrt{2}\)4, \(\sqrt{7-2\sqrt{10}}=\sqrt{5-2\sqrt{5}.\sqrt{2}+2}=\sqrt{\left(\sqrt{5}-\sqrt{2}\right)^2}=\left|\sqrt{5}-\sqrt{2}\right|=\sqrt{5}-\sqrt{2}\)5, \(\sqrt{15-6\sqrt{6}}=\sqrt{9-2.3.\sqrt{6}+6}=\sqrt{\left(3+\sqrt{6}\right)^2}=\left|3+\sqrt{6}\right|=3+\sqrt{6}\)Các câu còn lại tương tự nha!

Answer 2

6, \(\sqrt{8+2\sqrt{15}}=\sqrt{5+2\sqrt{5}.\sqrt{3}+3}=\sqrt{\left(\sqrt{5}+\sqrt{3}\right)^2}=\left|\sqrt{5}+\sqrt{3}\right|=\sqrt{5}+\sqrt{3}\)7, \(\sqrt{10-2\sqrt{21}}=\sqrt{7-2\sqrt{7}.\sqrt{3}+3}=\sqrt{\left(\sqrt{7}-\sqrt{3}\right)^2}=\left|\sqrt{7}-\sqrt{3}\right|=\sqrt{7}-\sqrt{3}\)8, \(\sqrt{11+2\sqrt{18}}=\sqrt{9+2\sqrt{9}.\sqrt{2}+2}=\sqrt{\left(\sqrt{9}+\sqrt{2}\right)^2}=\left|3+\sqrt{2}\right|=3+\sqrt{2}\)9, \(\sqrt{14-2\sqrt{33}}=\sqrt{11-2\sqrt{11}.\sqrt{3}+3}=\sqrt{\left(\sqrt{11}-\sqrt{3}\right)^2}=\left|\sqrt{11}-\sqrt{3}\right|=\sqrt{11}-\sqrt{3}\)Thử tự làm những câu còn lại rồi kiểm tra xem đúng hay sai nha!!!

Chúc bạn học tốt!!!

Answer 3

1/ \(=\sqrt{2+2\sqrt{2}+1}=\sqrt{\left(\sqrt{2}+1\right)^2}=\sqrt{2}+1\)

2/ \(=\sqrt{3-2\sqrt{3}+1}=\sqrt{\left(\sqrt{3}-1\right)^2}=\sqrt{3}-1\)

3/ \(=\sqrt{3+2\sqrt{6}+2}=\sqrt{\left(\sqrt{3}+\sqrt{2}\right)^2}=\sqrt{3}+\sqrt{2}\)

4/ \(=\sqrt{5-2\sqrt{10}+2}=\sqrt{\left(\sqrt{5}-\sqrt{2}\right)^2}=\sqrt{5}-\sqrt{2}\)

5/ \(=\sqrt{9-6\sqrt{6}+6}=\sqrt{\left(3-\sqrt{6}\right)^2}=3-\sqrt{6}\)

6/ \(=\sqrt{5+2\sqrt{15}+3}=\sqrt{\left(\sqrt{5}+\sqrt{3}\right)^2}=\sqrt{5}+\sqrt{3}\)

7/ \(=\sqrt{7-2\sqrt{21}+3}=\sqrt{\left(\sqrt{7}-\sqrt{3}\right)^2}=\sqrt{7}-\sqrt{3}\)

8/ \(=\sqrt{9+2\sqrt{18}+2}=\sqrt{\left(3+\sqrt{2}\right)^2}=3+\sqrt{2}\)

9/ \(=\sqrt{11-2\sqrt{33}+3}=\sqrt{\left(\sqrt{11}-\sqrt{3}\right)^2}=\sqrt{11}-\sqrt{3}\)